Question

A solid sphere of radius R is lying on a horizontal smooth surface. The sphere is hit by stick held horizontally at a height of $\frac{R}{2}$ above the center. The sphere moves forward with a velocity $v_0$ and angular velocity ${\omega }_0$ about its center. Then ${\omega }_0$ =

• A. $\frac{5v_0}{14R}$
• B. $\frac{15v_0}{4R}$
• C. $\frac{v_0}{R}$
• D. $\frac{5v_0}{4R}$

Answer 1

The correct option is D

$\frac{5v_0}{4R}$

Impulse $I=m{v}_0$ --- (1) and angular impulse about the center

$J=I\times \frac{R}{2}=\frac{2}{5}m{R}^2{\omega }_0$ --- (2)

Solving 1 and 2, we get $\frac{5v_0}{4R}$